3D Connexion Space Mouse stops responding during Blender operations
I don't think this is a 3D mouse issue, this is a well known general Blender limitation.

Most of those operators are modals (Knife Project, Extrude, Translate etc), and while they are running one cant access any other operators, until operation is terminated (that also includes viewport navigation operators like Move View or Rotate View). Bottom line is this is also an issue with regular mouse and keyboard.

Things may yet improve for the upcoming 2.8 series, but nothing is written in stone.